Recommender systems are one of the most successful applications of data mining and machine learning technology in practice. Academic research in the field is historically often based on the matrix completion problem formulation, where for each user-item-pair only one interaction (e.g., a rating) is considered. In many application domains, however, multiple user-item interactions of different types can be recorded over time. And, a number of recent works have shown that this information can be used to build richer individual user models and to discover additional behavioral patterns that can be leveraged in the recommendation process. In this work we review existing works that consider information from such sequentially-ordered user- item interaction logs in the recommendation process. Based on this review, we propose a categorization of the corresponding recommendation tasks and goals, summarize existing algorithmic solutions, discuss methodological approaches when benchmarking what we call sequence-aware recommender systems, and outline open challenges in the area. Sequence-Aware Recommender Systems